Finite Group Databasebeta

← #13040266

Subgroups — #13040266

Order 1280.

1096 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65758C211yesmaximal, characteristic, complemented
2C2×#65695C212yesmaximal
3C2×#65681C211yesmaximal, characteristic, complemented
4C4×#4027C211yesmaximal, characteristic
5#10604899C211yesmaximal, characteristic, complemented
6#10604232C212yesmaximal, complemented
7#10604191C211yesmaximal, characteristic, complemented
8#10604182C211yesmaximal, characteristic, complemented
9C4×C4⋊#170C211yesmaximal, characteristic, complemented
10#10603796C212yesmaximal, complemented
11#10603786C212yesmaximal, complemented
12C22×#704C2212yes—
13C22×#700C2212yes—
14C2×C4×C22⋊D5C411yescharacteristic
15C22×C4×Dic5C2211yescharacteristic
16C2×#4027C411yescharacteristic
17C2×#4027C2211yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×C22⋊#170C2212yes—
20#65758—24no—
21C2×#4004C2212yes—
22C2×#4004C2212yes—
23C2×#4004C2212yes—
24C2×#4003C2212yes—
25C2×C4⋊#170C2212yes—
26C2×C4⋊#170C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4⋊#170C2211yescharacteristic
30C2×C4×#170C2212yes—
31#65695—28no—
32#65681—24no—
33C4×C5×C22⋊C4C411yescharacteristic
34C22⋊C4×Dic5C411yescharacteristic
35C22⋊C4×Dic5C2211yescharacteristic
36C4×#685C411yescharacteristic
37C4×#683C411yescharacteristic
38C42×Dic5C2211yescharacteristic
39#64955C411yescharacteristic
40#64955C2211yescharacteristic
41#64938C411yescharacteristic
42#64938C2211yescharacteristic
43#64918C2212yes—
44#64918C2212yes—
45#64918C2212yes—
46#22650—51nomaximal, Sylow
47C23×C4×C5C2×C411yescharacteristic
48C22×C22⋊D5C2×C411yescharacteristic
49C23×Dic5C2×C411yescharacteristic
50C23×Dic5C2311yescharacteristic
51C22×C4×D5C2×C411yescharacteristic
52C22×C4×D5C2×C411yescharacteristic
53C22×C4×D5C2311yescharacteristic
54C2×#704—24no—
55C2×#704—24no—
56C2×#704—42no—
57C22×#170C2312yes—
58C22×#170C2312yes—
59C22×#170C2312yes—
60C22×#170C2312yes—
61C2×#700—24no—
62C2×#700—24no—
63C2×#700—42no—
64C2×C5×C22⋊C4C2×C411yescharacteristic
65C2×C5×C22⋊C4C2×C411yescharacteristic
66C2×C42×C5C2×C411yescharacteristic
67C2×C42×C5C2×C411yescharacteristic
68C2×C22⋊Dic5C2×C411yescharacteristic
69C4×C22⋊D5—24no—
70C2×#685C2×C411yescharacteristic
71C2×#685C2×C411yescharacteristic
72C2×#685C2×C411yescharacteristic
73C2×#683C2×C411yescharacteristic
74C2×#683C2×C411yescharacteristic
75C2×#683C2×C411yescharacteristic
76C2×C4×Dic5—22no—
77C2×C4×Dic5—22no—
78C2×C4×Dic5C2×C411yescharacteristic
79C2×C4×Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2×C411yescharacteristic
81C2×C4×Dic5C2×C411yescharacteristic
82C2×C4×Dic5C2×C411yescharacteristic
83C2×C4×Dic5C2×C411yescharacteristic
84C2×C4×Dic5C2311yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C2×C4×Dic5C2311yescharacteristic
87C2×C4×Dic5C2311yescharacteristic
88C2×C4×Dic5C2311yescharacteristic
89#4027—24no—
90#4027D414yes—
91#4027Q814yes—
92C42×D5—22no—
93C42×D5—22no—
94C22⋊#170—24no—
95#4004—24no—
96#4004—24no—
97#4004—42no—
98#4003—24no—
99C4⋊#170—24no—
100C4⋊#170—22no—
101C4⋊#170—22no—
102C4⋊#170—22no—
103C4⋊#170D414yescomplemented
104C4×#170—24no—
105C5×#95C2×C411yescharacteristic
106C5×#95C2×C411yescharacteristic
107#3963C2×C411yescharacteristic
108#3963C2×C411yescharacteristic
109#3963C2×C411yescharacteristic
110#3963C2×C411yescharacteristic
111C2×#436—52no—
112C2×#423—51no—
113C2×#423—51no—
114C42×D4—51no—
115#1939—52no—
116#1851—52no—
117#1851—52no—
118#1842—51no—
119#1797—51no—
120#1797—51no—
121C4×C4⋊C8—51no—
122C24×C5C22×C411yescharacteristic
123C23×D5C22×C411yescharacteristic
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5C22×C411yescharacteristic
128C22×C4×C5C22×C411yescharacteristic
129C22×C4×C5C22×C411yescharacteristic
130C22×C4×C5C22×C411yescharacteristic
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C22×C411yescharacteristic
133C2×C22⋊D5—22no—
134C2×C22⋊D5—22no—
135C2×C22⋊D5C4⋊C414yes—
136C22×Dic5—21no—
137C22×Dic5—21no—
138C22×Dic5—21no—
139C22×Dic5—21no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—41no—
143C22×Dic5C22×C411yescharacteristic
144C22×Dic5C22×C411yescharacteristic
145C22×Dic5C22×C411yescharacteristic
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C2×D412yes—
150C22×Dic5C2×Q812yes—
151C22×Dic5C2411yescharacteristic
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5—22no—
157C2×C4×D5—22no—
158C2×C4×D5—22no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—41no—
162C2×C4×D5C2×D412yes—
163C2×C4×D5C2×Q812yes—
164#704—48no—
165C2×#170—22no—
166C2×#170—22no—
167C2×#170—22no—
168C2×#170—22no—
169C2×#170—22no—
170C2×#170—22no—
171C2×#170—22no—
172C2×#170—22no—
173C2×#170—22no—
174C2×#170—22no—
175C2×#170—22no—
176C2×#170C2×D414yes—
177#700—48no—
178C5×C22⋊C4—22no—
179C5×C22⋊C4C4⋊C414yes—
180C42×C5—22no—
181C42×C5—22no—
182C22⋊Dic5—22no—
183#685—22no—
184#685—22no—
185#685C4⋊C414yes—
186#683—22no—
187#683C4⋊C414yes—
188#683M1614yescomplemented
189C4×Dic5—22no—
190C4×Dic5—22no—
191C4×Dic5—22no—
192C4×Dic5—22no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—21no—
197C4×Dic5—21no—
198C4×Dic5—21no—
199C4×Dic5—41no—
200C4×Dic5M1614yescomplemented
201C4×Dic5C2×D412yes—
202C4×Dic5C2×D412yes—
203C4×Dic5C2×Q812yes—
204C4×Dic5#4112yes—
205C22×M16—52no—
206C22×M16—52no—
207C2×C4×D4—51no—
208C2×C4×D4—51no—
209C2×C4×D4—51no—
210C22×C42—51no—
211C22×C42—51no—
212#436—108no—
213#423—104no—
214#423—104no—
215C2×C4⋊C8—51no—
216C2×C4⋊C8—51no—
217C2×C4⋊C8—51no—
218C2×C4⋊C8—51no—
219C2×C4⋊C8—52no—
220C2×C4⋊C8—52no—
221C2×C4⋊C8—52no—
222C2×C4⋊C8—52no—
223C2×C22⋊C8—52no—
224C2×C22⋊C8—52no—
225C2×C4×C8—52no—
226C4×C4⋊C4—51no—
227C4×C4⋊C4—51no—
228C4×C4⋊C4—51no—
229C4×C22⋊C4—51no—
230C4×C22⋊C4—51no—
231C4×C22⋊C4—51no—
232C4×C22⋊C4—51no—
233C4×C22⋊C4—51no—
234C4×C22⋊C4AGL(1,𝔽5)11yescharacteristic
235C43—51no—
236#336—52no—
237#336—52no—
238#336—52no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—21no—
244C23×C5—21no—
245C23×C5C2×C4⋊C412yes—
246C23×C5C23×C411yescharacteristic
247C22×D5—21no—
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—21no—
251C22×D5—21no—
252C22×D5—21no—
253C22×D5C2×C4⋊C412yes—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—44no—
267C2×C4×C5C2×C4⋊C412yes—
268C2×C4×C5C2×C4⋊C412yes—
269C2×C4×C5C4×D412yes—
270C2×C4×C5C2×M1612yes—
271C2×C4×C5C2×M1612yes—
272C2×C4×C5#13112yes—
273C22⋊D5—28no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—21no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—44no—
290C2×Dic5C2×C4⋊C412yes—
291C2×Dic5C2×C4⋊C412yes—
292C2×Dic5C4×D412yes—
293C2×Dic5C2×M1612yes—
294C2×Dic5C2×M1612yes—
295C2×Dic5C2×M1612yes—
296C2×Dic5C2×M1612yes—
297C2×Dic5C22×D411yescharacteristic
298C2×Dic5C22×D411yescharacteristic
299C2×Dic5C22×Q811yescharacteristic
300C2×Dic5C2×#4111yescharacteristic
301C2×Dic5H(5,𝔽2)11yescharacteristic
302C2×Dic52−1+411yescharacteristic
303C4×D5—22no—
304C4×D5—22no—
305C4×D5—22no—
306C4×D5—22no—
307C4×D5—44no—
308C4×D5—44no—
309#170—24no—
310#170—42no—
311#170—42no—
312#170—42no—
313C22×D4—51no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—51no—
318C23×C4—51no—
319C23×C4C2×AGL(1,𝔽5)11yescharacteristic
320C2×M16—104no—
321C2×M16—104no—
322C2×M16—104no—
323C2×M16—104no—
324C2×M16—202no—
325C2×M16—202no—
326C22×C8—52no—
327C22×C8—52no—
328C22×C8—52no—
329C22×C8—52no—
330C4×D4—54no—
331C4×D4—54no—
332C4×D4—104no—
333C4×D4—104no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C22⋊C4—51no—
338C2×C22⋊C4—51no—
339C2×C22⋊C4—51no—
340C2×C22⋊C4—51no—
341C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
342C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
343C2×C42—51no—
344C2×C42—51no—
345C2×C42—51no—
346C2×C42—51no—
347C2×C42—51no—
348C2×C42—51no—
349C2×C42—51no—
350C2×C42—51no—
351C2×C42—51no—
352C2×C42—51no—
353C2×C42—51no—
354C2×C42—102no—
355C2×C42—102no—
356C2×C42—102no—
357C2×C42—102no—
358C2×C42C2×AGL(1,𝔽5)11yescharacteristic
359C2×C42C2×AGL(1,𝔽5)11yescharacteristic
360C4⋊C8—54no—
361C4⋊C8—102no—
362C4⋊C8—102no—
363C4⋊C8—102no—
364C4⋊C8—104no—
365C4⋊C8—104no—
366C4⋊C8—104no—
367C4⋊C8—202no—
368C22⋊C8—104no—
369C22⋊C8—104no—
370C4×C8—104no—
371#95—51no—
372#95—51no—
373#95—51no—
374#95—51no—
375#95C2×AGL(1,𝔽5)11yescharacteristic
376#95C2×AGL(1,𝔽5)11yescharacteristic
377C22×C5—22no—
378C22×C5—22no—
379C22×C5—22no—
380C22×C5—41no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C22×C4⋊C411yescharacteristic
385C22×C5C2×C4×D411yescharacteristic
386C22×C5#52011yescharacteristic
387C22×C5C22×M1611yescharacteristic
388C22×C5C22×M1611yescharacteristic
389C22×C5C2×#13111yescharacteristic
390C22×C5#56811yescharacteristic
391C2×D5—22no—
392C2×D5—22no—
393C2×D5—22no—
394C2×D5—41no—
395C2×D5—41no—
396C2×D5—41no—
397C2×D5—41no—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—22no—
401C4×C5—41no—
402C4×C5—41no—
403C4×C5#43614yescomplemented
404Dic5—22no—
405Dic5—22no—
406Dic5—22no—
407Dic5—22no—
408Dic5—41no—
409Dic5#42314yescomplemented
410Dic5D4211yescharacteristic
411Dic5#54711yescharacteristic
412Dic5D4×Q811yescharacteristic
413Dic5#55411yescharacteristic
414C24—51no—
415C24C22×AGL(1,𝔽5)11yescharacteristic
416C2×D4—54no—
417C2×D4—102no—
418C2×D4—102no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—52no—
425C22×C4—52no—
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—51no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—102no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—201no—
449C22×C4—201no—
450C22×C4C22×AGL(1,𝔽5)11yescharacteristic
451C22×C4C22×AGL(1,𝔽5)11yescharacteristic
452C22×C4C22×AGL(1,𝔽5)11yescharacteristic
453C22×C4C22×AGL(1,𝔽5)11yescharacteristic
454C22×C4C22×AGL(1,𝔽5)11yescharacteristic
455C22×C4C22×AGL(1,𝔽5)11yescharacteristic
456M16—208no—
457M16—208no—
458C2×C8—54no—
459C2×C8—102no—
460C2×C8—102no—
461C2×C8—102no—
462C2×C8—102no—
463C2×C8—102no—
464C2×C8—102no—
465C2×C8—102no—
466C2×C8—102no—
467C2×C8—102no—
468C2×C8—102no—
469C2×C8—102no—
470C4⋊C4—54no—
471C4⋊C4—54no—
472C4⋊C4—102no—
473C22⋊C4—22no—
474C22⋊C4—54no—
475C22⋊C4—102no—
476C22⋊C4—102no—
477C22⋊C4—102no—
478C22⋊C4C4⋊AGL(1,𝔽5)14yes—
479C42—22no—
480C42—22no—
481C42—54no—
482C42—52no—
483C42—52no—
484C42—52no—
485C42—52no—
486C42—101no—
487C42—101no—
488C42—101no—
489C42—101no—
490C42—102no—
491C42—101no—
492C42—102no—
493C42—102no—
494C42—101no—
495C42—102no—
496C42—201no—
497C2×C5—42no—
498C2×C5D4×C4⋊C411yescharacteristic
499C2×C5C2×#42311yescharacteristic
500C2×C5#290611yescharacteristic
501C2×C5C2×#43611yescharacteristic
502C2×C5D4×M1611yescharacteristic
503C2×C5#298911yescharacteristic
504C2×C5#299111yescharacteristic
505D5—42no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—52no—
513C23—101no—
514C23—101no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23—101no—
519C23C2×C4⋊AGL(1,𝔽5)12yes—
520C23C23×AGL(1,𝔽5)11yescharacteristic
521D4—108no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—52no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—51no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—51no—
542C2×C4—51no—
543C2×C4—51no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—204no—
568C2×C4—204no—
569C2×C4—204no—
570C2×C4D5⋊M1612yes—
571C2×C4D5⋊M1612yes—
572C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
573C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
574C2×C4#413112yes—
575C2×C4D4×AGL(1,𝔽5)12yes—
576C8—104no—
577C8—202no—
578C8—202no—
579C8—202no—
580C5#2265011yescharacteristic, complemented, Sylow
581C22—22no—
582C22—22no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—102no—
589C22—102no—
590C22—102no—
591C22—201no—
592C22—201no—
593C22—201no—
594C22—201no—
595C22C2×D5⋊M1611yescharacteristic
596C22C2×D5⋊M1611yescharacteristic
597C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
598C22C2×#413111yescharacteristic
599C22C2×D4×AGL(1,𝔽5)11yescharacteristic
600C22#6626411yescharacteristic
601C22#6626611yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—41no—
606C4—41no—
607C4—51no—
608C4—51no—
609C4—51no—
610C4—51no—
611C4—54no—
612C4—102no—
613C4—102no—
614C4—102no—
615C4—102no—
616C4—201no—
617C4#6569514yescomplemented
618C2—42no—
619C2—202no—
620C2D5⋊#42311yescharacteristic
621C2C2×#6569511yescharacteristic
622C2#1061712111yescharacteristic
623C2#1061713711yescharacteristic
624C2#1061715011yescharacteristic
625C2#1061717011yescharacteristic
626C2D4×C4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC4×C5×C22⋊C4C4
prime radicalC22×C22⋊D5C2×C4
cosocleC22×Dic5C24
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5#22650
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#65758C2semidirect
3. C2×#65681C2semidirect
5. #10604899C2semidirect
6. #10604232C2semidirect
7. #10604191C2semidirect
8. #10604182C2semidirect
9. C4×C4⋊#170C2semidirect
10. #10603796C2semidirect
11. #10603786C2semidirect
103. C4⋊#170D4semidirect
188. #683M16semidirect
200. C4×Dic5M16semidirect
403. C4×C5#436semidirect
409. Dic5#423semidirect
580. C5#22650semidirect
617. C4#65695semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#657582
C2×#656952
C2×#656812
C4×#40272
#106048992
#106042322
#106041912
#106041822
C4×C4⋊#1702
#106037962
#106037862
#226505